The Borsuk-Ulam theorem and bisection of necklaces

Source abstract

The Borsuk-Ulam theorem of topology is applied to a problem in discrete mathematics. A bisection of a necklace with k k colors of beads is a collection of intervals whose union captures half the beads of each color. Every necklace with k k colors has a bisection formed by at most k k cuts. Higher-dimensional generalizations are considered.